"We didn't expect that result... it's better than them winning," Giggs, after hearing of Chelsea's 0-1 slip-up, told MUTV.
"We've got to do our own job, not worry about the teams around us. It's still in our hands."
That said, Giggs wasn't taking defeat at Fulham lightly, especially as it confirmed back-to-back defeats in the league for the first time since the 2004/05 season.
"We're obviously disappointed with the result. After losing last weekend, we wanted to come here and put on a good performance.
"We didn't do that in the first half - our passing was sloppy and our movement wasn't good enough. We just couldn't get it going, the tempo wasn't good."
Giggs had praise for goalkeeper Edwin van der Sar on his return to Craven Cottage.
He added: "Going a goal behind and down to ten men, we had to arrange our shape a little bit differently. We came out and played a lot better in the second half. We were on top, we created some good chances and their keeper made a couple of good saves. Had one of those efforts gone in then we could have gone on to win it but it wasn't to be.
"Some of our lads now go away for the international break. Hopefully we won't have any injuries and we can get back on track against Villa."